Abstract

Taking into account the effect of the low-energy band structure of carbon nanotubes (CN), we develop the theories of CN field and thermionic emissions. We give the analytic field and thermionic emissionequations for both metal and semiconducting CNs. These theories modify the conventional Fowler–Nordheim (FN) and Murphy–Good (MG)theories. For large-diameter CNs and high fields, the field-emissionequation reduces the FN-type field-emissionequation. For small-diameter CNs and low fields, the field-emissionequation goes beyond the FN-type behavior, which provides a possible way to understand the non-FN behavior observed in experimental results. Based on these theories, we give the electron-emission phase diagram on the field, thermionic, and intermediate emissions in the field-temperature space, whose boundaries have a slight shift to the corresponding boundaries of MG’s theory. These differences come from the energy-band structure difference between CN and conventional emitters. This theory provides an understanding of field and thermionic emissions for nanoscale materials.

Received 10 September 2009Accepted 04 January 2010Published online 31 March 2010

Acknowledgments:

This work was supported financially by the National Natural Science Foundation of China (Grant No. 10774194), the National Basic Research Program of China (973 Program No. 2007CB935501), and the Advanced Academic Center of Sun Yat-Sen University.